Complex Analysis of Real Functions


IV: Non-Integrable Real Functions

Jorge L. deLyra1

Department of Mathematical Physics, Physics Institute, University of São Paulo

September 1, 2017


Abstract:

In the context of the complex-analytic structure within the unit disk centered at the origin of the complex plane, that was presented in a previous paper, we show that a certain class of non-integrable real functions can be represented within that same structure. In previous papers it was shown that essentially all integrable real functions, as well as all singular Schwartz distributions, can be represented within that same complex-analytic structure. The large class of non-integrable real functions which we analyze here can therefore be represented side by side with those other real objects, thus allowing all these objects to be treated in a unified way.